Assume a general angular velocity vector defined in the body frame coordinate systems B = {b?,b?, b3} such that @=w?b? + w?b? + w3b3. Prove the following identity w xb? wxb? [w x b3] [B? -[x] b? == b3

Assume a general angular velocity vector $?$ defined in the body frame coordinate systems $B = {\hat{b}_{1}, \hat{b}_{2}, \hat{b}_{3}}$ such that $? = ?_{1} \hat{b}_{1} + ?_{2} \hat{b}_{2} + ?_{3} \hat{b}_{3}$ . Prove the following identity $? ? ? \times b_{1} ? \times b_{2} ? \times b_{3} ? ? = ? [? \times] ? ? \hat{b}_{1} \hat{b}_{2} \hat{b}_{3} ? ?$

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Assume a general angular velocity vector defined in the body frame coordinate systems B = {b?,b?, b3} such that @=w?b? + w?b? + w3b3. Prove the following identity w xb? wxb? [w x b3] [B? -[x] b? == b3

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Assume a general angular velocity vector

?

defined in the body frame coordinate systems

B = {\hat{b}_{1}, \hat{b}_{2}, \hat{b}_{3}}

such that

? = ?_{1} \hat{b}_{1} + ?_{2} \hat{b}_{2} + ?_{3} \hat{b}_{3}

. Prove the following identity

? ? ? \times b_{1} ? \times b_{2} ? \times b_{3} ? ? = ? [? \times] ? ? \hat{b}_{1} \hat{b}_{2} \hat{b}_{3} ? ?

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